Exact Solutions for Steady State Incompressible Magnetic Reconnection

Abstract

The problem of steady state magnetic reconnection in incompressible, resistive plasmas is addressed. It is shown that families of exact analytic solutions can be derived by exploiting the formal symmetry between the magnetic field lines and the streamlines of the flow. These solutions, while incorporating previous models for antiparallel magnetic merging, assume no inherent topological symmetry for the reconnective geometry. It is demonstrated that fast reconnection occurs within a narrow X-type configuration defined by the intersection of two separatrix lines. One separatrix line is undistinguished physically, but the other is contiguous with a global current sheet across which there is no plasma flow. The implication is that fast reconnection is more likely to be associated with strong shearing motions close to the neutral point rather than with the conventional stagnation point flow topology.

Exact Steady State Reconnection Solutions in Weakly Collisional Plasmas

“…As in Craig & Henton (1995), we observe that ''fast'' reconnection solutions, for which the electric field E at the X-point scales independently of the resistivity, can in principle always be constructed by a suitable choice of external boundary conditions. However, severe pressure constraints on the solution effectively limit the range of parameter space for which such fast solutions are valid (see Craig & Henton 1995;Craig & Watson 2000).…”

“…One interesting advance in recent years was the discovery by Craig & Henton (1995) of an exact reconnection solution for resistive single-fluid plasmas. This simple two-dimensional solution has since been modified to include the effects of threedimensionality, time dependence, and different spatial geometries (Craig & Fabling 1996, 1998Watson & Craig 2002).…”

The impact of small-scale turbulence on laminar magnetic reconnection

“…8 We have found that for modest levels of turbulence, the underlying large-scale features of the laminar solution are robust and even the intrinsic scalings of the problem with plasma resistivity are retained. Some modest enhancement of the energy dissipation is observed, but this is mainly due to the additional small-scale structures inherent in the turbulent initial conditions.…”

“…III we summarize the analytic solution of Ref. 8, and in Sec. IV we develop a simple analytic timedependent solution that indicates the behavior of the individual Fourier modes in a full 2D simulation.…”

“…Another approach is to explore the new generation of analytic resistive MHD reconnection solutions. 8,9 These are valid for arbitrarily small resistivities in both twodimensional ͑2D͒ and three-dimensional ͑3D͒ geometries, and provide a convenient platform for energy release studies and particle acceleration calculations. 10,11 Questions concerning the dynamic accessibility of the analytic solutions have recently been addressed, [12][13][14] but so far the robustness of the solutions to turbulence has not been investigated-despite turbulent resistivities being invoked as a remedy for unphysically high current densities.…”